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If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3...

If the lines `(x-1)/(-3)=(y-2)/(2k)=(z-3)/2`and `(x-1)/(3k)=(y-1)/1=(z-6)/(-5)`are perpendicular, find the value of k.

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The direction ratios of given lines are
`(-3,2k,2)` and `(3k,1,-5)`
The lines of direction ratios, ` a_(1),b_(1),c_(1)` and ` a_(2),b_(2),c_(2)` will be perpendicular.
If `a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2)=0`
`:. (-3)xx(3k)+(k)xx1+2xx(-5)=0`
`rArr -9k+2k-10=0`
`rArr 7k = -10 rArr k = (-10)/(7)`
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If the lines (x-1)/(-3)=(y-2)/(-2k)=(z-3)/2 and (x-1)/k=(y-2)/1=(z-3)/5 are perpendicular, find the value of k and hence find the equation of plane containing these lines.

If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(-2) and (x-1)/(3k)=(y-5)/1=(z-6)/(-5) are at right angle, then find the value of k .

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If the line (x-1)/(-3) = (y-2)/(2k) = (z-3)/( 2) and (x-1)/( 3k) = (y-5)/(1) = (6-z)/(5) are mutually perpendicular, then k is equal to

Find the value of k so that the lines (1-x)/(3) = (y-2)/(2k) = (z-3)/(2) and (1+x)/(3k) = (y-1)/(1) = (6-z)/(7) are perpendicular to each other.

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In sub-parts (i) and (ii) choose the correct option and in sub-parts (iii) to (v), answer the questions as instructed. Find k so that the lines (1-x)/(3)=(y-2)/(2k)=(z-3)/(2) and (x-1)/(3k)=(y-5)/(1)=(6-z)/(5) are at right angles .

The lines (x-2)/(1) = (y-3)/(1) =(z-4)/(-k) and (x-3)/(k)=(y-4)/(1) = (z-5)/(1) are coplanar if the values of k are

The equation of the plane passing through the poit of intersection of the lines (x-1)/(3)=(y-2)/(1)=(z-3)/(2),(x-3)/(1)=(y-1)/(2)=(z-2)/(3) and perpendicular to the line (x-2)/(2)=(y-3)/(3)=(z-2)/(1) is P = 0. If the distance of the point (1, 1, 3) from P = 0 is k units, then the value of (k^(2))/(2) is equal to

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NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Miscellaneous Exercise
  1. Find the equation of a line parallel to x-axis and passing through ...

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  2. If the coordinates of the points A ,B ,C ,D are (1,2,3),(4,5,7),(-4,3,...

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  3. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...

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  4. Find the vector equation of the line passing through (1, 2, 3) and ...

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  5. Write the vector equation of the plane, passing through the point (a ,...

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  6. Find the shortest distance between lines vecr = 6hati+2hatj+2hatk+lam...

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  7. Find the coordinate of the point where the line through (5, 1, 6) and ...

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  8. Find the coordinates of the point where the line through (5, 1, 6) ...

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  9. Find the coordinates of the point where the line through (3, -4, -5...

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  10. Find the equation of the plane passing through the point (-1, 3, 2)...

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  11. If the points (1," "1," "p)" "a n d" "(" "3," "0," "1) be equidistant ...

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  12. Find the equation of the plane passing through the line of intersectio...

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  13. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

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  14. Find the equation of the plane which contains the line of intersection...

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  15. Find the distance of the point (-1,-5,-10) from the point of the inter...

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  16. Find the vector equation o the line passing through (1,2,3) and parall...

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  17. Find the vector equation of line passing through the point (1, 2, -4) ...

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  18. Prove that if a plane has the intercepts a ,\ b ,\ c\ a n d\ is at a ...

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  19. Distance between the two planes 2x+3y +4z =4 and 4x+6y +8z=12 is

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  20. The planes 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are

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